The invention relates in general to fuel supply system for internal combustion engines having a throttle valve disposed in an air intake tube, and more particularly, to an air valve for varying the cross-sectional area of a throttle valve by-pass. An air valve is already known which, in order to influence the fuel-air mixture during engine overrunning, responds to the pressure drop occurring in the intake tube upon the abrupt closing of the throttle valve and delivers a predetermined air quantity to the closed throttle valve. This quantity of air is sufficient to maintain combustion in the individual cylinders of the internal combustion engine during overrunning. A further air valve is also known which permits an additional air quantity to flow past the throttle valve via a bypass in order to improve the starting behavior of the engine. Thus, to fulfill both of these functions, two separate air valves and a large number of connections are required with devices of the prior art.